M. T. Barriuso

Impurity-ligand distances derived from magnetic resonance and optical parameters

Non empirical methods for obtaining information from EPR, ENDOR and optical data on the true impurity-ligand distance,R, as well as on the true variations, ΔR, induced by chemical and hydrostatic pressures, phase transitions in the host material and temperature changes are discussed through this work. Special attention is addressed to spectroscopic parameters of d-impurities whose dependence onR can reasonably be calculated theoretically for the superhyperfine (shf) tensor or the lowest optical transitions but not for fine structure terms. In the case of impurities with unpaired σ-electrons it is shown that the isotropic shf constant,As, is specially sensitive toR changes. The microscopic origin of this fact is discussed in detail. Determination of trueR values from experimentalAs has been carried out for impurities like Mn2+ or Ni+ with encouraging results. In the case of Mn2+ in fluorides, results obtained by this method coincide with those reached through EXAFS and the analysis of the experimental 10 Dq. Finally, for some selected complexes, a view is offered on the dependence of several EPR and optical parameters upon metal-ligand distances. The main conclusion is that ΔR values of the order of 0.1 pm can be detected using EPR and optical parameters thus improving by an order of magnitude the sensitivity reached through EXAFS. In particular the use of ENDOR allows one to measure ΔR values close to 0.01 pm.

The Huang-Rhys factor S(a1g) for transition-metal impurities: a microscopic insight

A microscopic model for evaluating the Huang-Rhys factor S(a1g) associated with the symmetric mode of a transition-metal impurity M in insulators is proposed. It is applied to the first excited states of Cr3+, V2+, Mn2+ and Cu2+. Theoretical calculated values of the exponent n indicate that it varies slightly along the ligand series F- to Cl- to Br- giving rise to an increase in S(a1g). This explains why the Stokes shift of systems involving MBrN units can be similar or higher than the corresponding shifts of MFN complexes.

Microscopic insight into properties and electronic instabilities of impurities in cubic and lower symmetry insulators: the influence of pressure

This article reviews the microscopic origin of properties due to transition-metal (TM) impurities, M, in insulator materials. Particular attention is paid to the influence of pressure upon impurity properties. Basic concepts such as the electronic localization in an MX(N) complex, the electrostatic potential, V(R), arising from the rest of the lattice ions or the elastic coupling of the complex to the host lattice are initially exposed. The dependence of optical and magnetic parameters on the impurity-ligand distance, R, in cubic lattices is discussed in a first step. Emphasis is put on the actual origin of the R dependence of 10Dq. Examples revealing that laws for strict cubic symmetry cannot in general be transferred to lower symmetries are later given. This relevant fact is shown to come from allowed hybridizations like nd-(n+1)s as well as the influence of V(R). As a salient feature the different colour in ruby and emerald is stressed to arise from distinct V(R) potentials in Al(2)O(3) and Be(3)Si(6)Al(2)O(18). The last part of this review deals with electronic instabilities. The phenomena associated with the Jahn-Teller (JT) effect in cubic lattices, the origin of the energy barrier among equivalent minima and the existence of coherent tunnelling in systems like MgO:Cu(2+) are discussed. An increase of elastic coupling is pointed out to favour a transition from an elongated to a compressed equilibrium conformation. Interestingly the equilibrium geometry of JT ions in non-cubic lattices is shown to be controlled by mechanisms different to those in cubic systems, V(R) playing again a key role. The relevance of first principles calculations for clarifying the subtle mechanisms behind off-centre instabilities is also pointed out. Examples concern monovalent and divalent TM impurities in lattices with the CaF(2) structure. The instability due to the transition from the ground to an excited state is finally considered. For complexes with significant elastic coupling vibrational frequencies and the Stokes shift are expected to undergo bigger changes through a chemical rather than a hydrostatic pressure. The reduction of Huang-Rhys factors upon increasing the pressure is discussed as well.

Spectrochemical Series and the Dependence of Racah and 10Dq Parameters on the Metal−Ligand Distance: Microscopic Origin

The origin of the spectrochemical series and the different dependence of crystal-field splitting (10Dq) and Racah parameters on the metal-ligand distance, R, is explored through ab initio calculations on Cr(3+)-doped K2NaScF6, Cs2NaYCl6, Cs2NaYBr6, and Cs2NaYI6 lattices. For this purpose both periodic and cluster calculations have been performed. An analysis of ab initio results proves that 10Dq values mostly come from the small admixture of deep nLs ligand orbitals present in the antibonding eg(∼ x(2)-y(2),3z(2)-r(2)) level and not from the dominant covalency with valence nLp ligand orbitals, which is actually responsible for the reduction of Racah parameters. This study thus reveals the microscopic origin of the stronger dependence upon R of 10Dq when compared to that observed for Racah parameters, thus explaining why electronic transitions which are 10Dq-independent give rise to sharp optical bands. As a salient feature, while the covalency with nLp levels increases significantly on passing from CrF6(3-) to CrI6(3-), the nLs admixture in eg is found to be practically unmodified. This fact helps to understand the progressive decrease of 10Dq through the series of CrF6(3-), CrCl6(3-), CrBr6(3-), and CrI6(3-) complexes embedded in the corresponding host lattices when compared at the corresponding equilibrium distance at zero pressure. The growing importance of the nLs admixture is well-depicted using deformation density diagrams on passing from the ground state (4)A2(t2g(3)) to the (4)T2(t2g(2)eg) excited state depicted at several R values.

Crystal-field and charge transfer transitions due to Cr3+ ions in fluorides

The metal-ligand equilibrium distance, Re, vibrational frequencies, crystal-field (CF) and charge transfer (CT) transition energies, Huang–Rhys factors, Stokes shift, as well as oscillator strengths of allowed CT transitions due to Cr3+ in fluorides, have been investigated using density functional theory. CrF63− and CrF6K8K611+ clusters simulating Cr3+ in the K3CrF6 lattice have been used. In the CrF6K8K611+ cluster the computed equilibrium distance using a generalized gradient approximation functional is Re=1.88 A and an overall agreement with experimental spectroscopic parameters is achieved. As salient feature it is pointed out that 6% errors in Re can lead to errors of ∼40% and ∼25%, respectively, in the calculated vibrational frequencies and the 10 Dq parameter. Moreover the force constant, kT, involved in the A1g symmetrical mode at the equilibrium distance is shown to be mainly determined by the interaction between the central ion and the ligands while the interaction between the latter ones and K+ neighbors leads to a contribution which is about 25% of kT. The calculated oscillator strengths confirm that the transitions involving the ligand t1u orbital and the antibonding eg*↑ and eg*↓ ones should be the most intense among the nine allowed CT transitions. Moreover, CT transitions connecting two orbitals which do not have the same σ or π character are found to display an oscillator strength much smaller than for the rest of the cases. This idea is shown to be also valid for other transition-metal complexes. The computed Huang–Rhys factor associated with the A1g mode, SA, for the lowest CT transition is shown to be about ten times higher than that corresponding to the 4T2g CF state and explains the experimental bandwidth. The origin of this important difference is discussed. Finally, the electronic relaxation in the first 4T2u CT state is shown to induce an important decrement (∼40%) of the 4A2g→4T2u transition energy and an increase of the total charge on the central ion of only 0.2 e.The metal-ligand equilibrium distance, Re, vibrational frequencies, crystal-field (CF) and charge transfer (CT) transition energies, Huang–Rhys factors, Stokes shift, as well as oscillator strengths of allowed CT transitions due to Cr3+ in fluorides, have been investigated using density functional theory. CrF63− and CrF6K8K611+ clusters simulating Cr3+ in the K3CrF6 lattice have been used. In the CrF6K8K611+ cluster the computed equilibrium distance using a generalized gradient approximation functional is Re=1.88 A and an overall agreement with experimental spectroscopic parameters is achieved. As salient feature it is pointed out that 6% errors in Re can lead to errors of ∼40% and ∼25%, respectively, in the calculated vibrational frequencies and the 10 Dq parameter. Moreover the force constant, kT, involved in the A1g symmetrical mode at the equilibrium distance is shown to be mainly determined by the interaction between the central ion and the ligands while the interaction between the latter ones and K+...

Puzzling absence of hyperfine interaction in the D4hRhCl64− centre: role of the 4d–5s hybridization in Rh2+ centres

The amazing absence of hyperfine interaction in EPR spectra of the tetragonally elongated RhCl64− centre in NaCl is explored through the present work. In addition to the core polarization contribution it is shown that there is another isotropic contribution from the small 5s admixture in the a1g*(≈ 3z2 − r2) level. These two contributions together with the anisotropic ones are shown to lead to a null hyperfine tensor for a 5s admixture of only ~ 1.5%. Density functional calculations reveal that such an admixture is strongly sensitive to the tetragonality of the RhCl64− unit. Writing the axial (Rax) and equatorial (Req) Rh2+–Cl− distances as Rax = R0 + 2a and Req = R0 − a it is shown that (i) the 5s admixture is proportional to a2 (for a≤25 pm), a fact which can be accounted for through a simple model; (ii) relative variations of Req and Rax of only −0.4 and 0.8% lead to a hyperfine constant of 7 MHz. The present results are shown to shed some light on EPR data of the orthorhombic RhCl64− complex with two cis-equatorial Na+ vacancies in the fourth shell. It is concluded that the hyperfine interaction measured for this centre can be explained in terms of the small strain induced by equatorial Na+ vacancies upon the RhCl64− unit. This idea can also explain the ~ 2% decrement of the isotropic axial superhyperfine constant when compared with that for the tetragonal RhCl64− centre.

How do the electronic properties of d9 impurities depend on metal-ligand distances? Application to Ni+, Cu2+ and Ag2+ systems

The dependence of the optical and spin-Hamiltonian parameters of NiF65- and NiF43- D4h units, with a b1g* ( approximately x2-y2) unpaired electron, upon the equatorial (Req) and axial (Rax) Ni+-F- distances has been studied through multiple-scattering X alpha and self-consistent charge extended Huckel methods. Both methods lead to the following main conclusions: (i) A charge-transfer transition like eu( pi + sigma ,eq) to b1g*( approximately x2-y2) (termed Eu) is more sensitive than a crystal-field one like b2g* ( approximately xy) to b1g*( Delta 1) or eg* to b1g*( Delta 2) to variations in Req. The change experienced by Eu mainly reflects that of Vel(M)-Vel(L), where Vel(M) and Vel(L) are the electrostatic potentials experienced by an electron placed on metal and ligands, respectively, (ii) As regards the unpaired spin densities onto nLp and nLs ligand valence orbitals (termed fsigma and fs respectively), it is found that fsigma >>fs but fs is much more sensitive than fsigma to changes in Req. The microscopic origin of this relevant fact is explained in detail. (iii) The removal of axial ligands, keeping Req constant, induces a decrease of Eu as a result of the diminution of the electrostatic repulsion, Vel (M), and produces a slight increase of Delta 1 and a more important one of Delta 2. (iv) The dependence of g//-g0 and gperpendicular to -g0 on Req essentially reflects that of Delta 1-1 and Delta 2-1, respectively, because of the low covalency (fsigma approximately=2%).

Optical excitations and coupling constants in FeO42− and CrO44− complexes in oxides: Density functional study

The experimental crystal field (CF) and charge transfer (CT) spectra due to Fe6+-doped K2XO4 (X=S, Se, Cr) and Cr4+ in oxides have been investigated by density functional (DF) calculations on FeO42− and CrO44− complexes at different values of the metal–ligand distance, R. To this aim the coupling constants, Aα and Ae, with the A1 and the Jahn–Teller E modes have also been calculated. The present results explain reasonably the transition energies and coupling constants observed for Fe6+ and Cr4+ in oxides and account for the following experimental features: (i) The different nature of the first CF and CT excitations observed on passing from Fe6+ to Cr4+ in oxides. (ii) Why for Fe6+ in oxides the dominant coupling is with the E mode for the CF states while with the A1 mode for CT states. (iii) Why on going from Cr4+ to Fe6+ in oxides the coupling constant Aα of CT states decreases while the opposite is found for CF ones. The role played by the covalency on these questions is explained on simple grounds, str...

Electronic structure of Ag2+ impurities in halide lattices

The composition of electronic levels as well as optical transitions associated with AgCl64- and AgF64- complexes have been studied through MS-X alpha and SCCEH calculations performed as a function of equatorial (Req) and axial (Rax) metal-ligand distances. The scheme and composition of levels for AgCl64- is rather different from that for AgF64- and other more ionic systems. The first transition for KCl:Ag2+ (observed at 12 500 cm-1) is assigned to a jump involving the 5a1g orbital which is mainly built (about 70%) from 3p orbitals of axial chlorine atoms. Aside from explaining reasonably the five optical bands experimentally observed for KCl:Ag2+, the present work indicates that the first allowed charge-transfer transition of AgF64- would lie in the ultraviolet region and confirms that the unpaired electron in AgCl64

Optical and vibrational properties of MnF64− complexes in cubic fluoroperovskites: insight through embedding calculations using Kohn–Sham equations with constrained electron density

spends a little more time on equatorial ligands than on the central ion. All these results are consistent with a high value ( chi =2.8) for the optical electronegativity of Ag2+. The dependence of electronic transitions (and also of unpaired spin densities fsigma and fs) on Req and Rax is found to be rather similar for both AgF64- and AgCl64- complexes. The relation between such a dependence and the band widths of optical transitions is outlined.